Image forming apparatus

ABSTRACT

An incidence angle of laser light with respect to a photosensitive member in a main-scanning direction is different depending on an exposure position. Hence, the spot shape of the laser light on the photosensitive member is different in the main-scanning direction. A filter coefficient is changed in the main-scanning direction, and image data is corrected with the filter coefficient.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Continuation of co-pending U.S. patent applicationSer. No. 14/785,290, filed Oct. 16, 2015, which is a U.S. national stageapplication of International Patent Application No. PCT/JP2014/058853with international filing date Mar. 27, 2014 and which claims foreignpriority benefit of Japanese patent application No. 2013-087877 filedApr. 18, 2013, all of which are hereby incorporated by reference hereinin their entirety.

TECHNICAL FIELD

The present invention relates to an electrophotographic image formingapparatus, such as a digital copier, a multifunction device, or a laserprinter.

BACKGROUND ART

An electrophotographic image for apparatus forms an image by developingan electrostatic latent image formed on a photosensitive member with atoner. The image forming apparatus includes an optical scanning device.An electrostatic latent image is formed on the photosensitive member byscanning with laser light emitted from the optical scanning device onthe basis of image data. The optical scanning device includes arotatable polygonal mirror that deflects laser light emitted from alight source, and an optical member such as a lens or a mirror thatguides the laser light deflected by the rotatable polygonal mirror ontothe photosensitive member.

The photosensitive characteristics of the surface of the photosensitivemember slightly vary depending on the position of the surface of thephotosensitive member. Even if the photosensitive member is exposed tolaser light with the same light quantity, the density of an output imagemay be uneven due to the unevenness of the photosensitivecharacteristics of the surface of the photosensitive member.

To address the problem, PTL 1 discloses an image forming apparatus thatcorrects image data in accordance with a scanning position (exposureposition) with laser light on a photosensitive member. With the imageforming apparatus described in PTL 1, the unevenness of the density ofthe output image due to the unevenness of the photosensitivecharacteristics of the surface of the photosensitive member can berestricted.

CITATION LIST Patent Literature

PTL 1: Japanese Patent Laid--Open No. 2010-131989

SUMMARY OF INVENTION Technical Problem

However, the electrophotographic image forming apparatus has a problemin addition to the aforementioned problem. As shown in FIG. 21, theincident angle of the laser light with respect to the photosensitivemember is different depending on the exposure position in a direction inwhich the laser light scans the photosensitive member (main-scanningdirection) shown in FIG. 21(a). Owing to this, the spot shape of thelaser light on the photosensitive member is different depending on theposition in the main-scanning direction. Also, the spot shape of thelaser light on the photosensitive member may not be uniform in themain-scanning direction depending on the arrangement accuracy of thelens or mirror that guides the laser light to the photosensitive member.Due to the unevenness of the spot shape of the laser light in themain-scanning direction, it may be difficult to obtain a good image. Inparticular, in a case in which an image is formed at a screen angleinclined to the main-scanning direction, for example, as indicated by+45′ of L2 and −45° of R2 in FIG. 21(c), the image quality of the outputimage may be decreased due to the different orientations of the sportshapes of the laser light and the different screen angles.

Solution to Problem

The present invention is made in light of the above-described problems,and there is provided an image forming apparatus including a lightsource configured to emit light beam for exposing a photosensitivemember to light; deflecting means for deflecting the light beam so thatthe light beam scans the photosensitive member; optical means forguiding the light beam deflected by the deflecting means to thephotosensitive member; data generating means for generating pixel datacorresponding to each pixel included in an output image; outputtingmeans for outputting correction data for correcting unevenness of apotential distribution of an electrostatic latent image centered at atarget pixel formed on the photosensitive member by exposure of thephotosensitive member to the light beam in a scanning direction in whichthe light beam scans the photosensitive member, the correction datacorresponding to a position of the target pixel in the scanningdirection, the outputting unit outputting the correction data beingindicative of an amount of change in potential at the position of thetarget pixel caused by exposure of a surrounding pixel located aroundthe target pixel to the light beam; correcting means for correctingpixel data of the target pixel on the basis of the correction data andthe pixel data of the target pixel; and control means for controllingthe light source on the basis of the pixel data of the target pixelcorrected by the correcting means, to form the target pixel. Also, thereis another image forming apparatus including a light source configuredto emit light beam for exposing a photosensitive member to light;deflecting means for deflecting the light beam so that the light beamscans the photosensitive member; optical means for guiding the lightbeam deflected by the deflecting means to the photosensitive member;data generating means for generating pixel data corresponding to eachpixel included in an output image; outputting means for outputtingcorrection data for correcting unevenness of a potential distribution ofan electrostatic latent image centered at a target pixel formed on thephotosensitive member by exposure of the photosensitive member to thelight beam in a scanning direct on in which the light beam scans thephotosensitive member, the correction data being indicative of an amountof change in potential at a pixel position of a surrounding pixelsurrounding the target pixel caused by exposure of the target pixel;correcting means for correcting pixel data of the target pixel, andpixel data of the target pixel corrected on the basis of the correctiondata; and control means for controlling the light source on the basis ofthe pixel data corrected by the correction means, to form the targetpixel.

ADVANTAGEOUS EFFECTS OF INVENTION

With the invention, the decrease in image quality due to the unevennessof the spot shape of the laser light in the main-scanning direction canbe restricted by correcting the image data with use of thetwo-dimensional filter.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic cross-sectional view of an image formingapparatus.

FIG. 2 is a schematic configuration diagram of an optical scanningdevice.

FIG. 3 is a control block diagram of an image processor and a laserdrive included in the image forming apparatus according to a firstembodiment.

FIG. 4 is a block diagram of an exposure modulator.

FIG. 5 provides explanatory views of LUT.

FIG. 6 illustrates a two-dimensional gauss distribution diagram and aFourier transform result of the two-dimensional gauss distribution.

FIG. 7 illustrates exposure distribution. characteristic data.

FIG. 8 illustrates differential data between the exposure distributioncharacteristic data and reference characteristic data.

FIG. 9 is correction data generated on the basis of the differentialdata.

FIG. 10 is a schematic illustration of filter coefficients.

FIG. 11 is a matrix diagram of the filter coefficients.

FIG. 12 illustrates as effect provided by a two-dimensional filter.

FIG. 13 provides control block diagrams of an image processor includedin an image for apparatus according to a second embodiment.

FIG. 14 is a matrix diagram of filter coefficients.

FIG. 15 is a conceptual diagram of a first operation.

FIG. 16 illustrates an example of filter coefficients stored in a ROM ofthe image forming apparatus according to the second embodiment.

FIG. 17 is a conceptual diagram of a second operation.

FIG. 18 illustrates a change in spot shape in accordance withdefocusing.

FIG. 19 is a control block diagram of an image processor included in animage forming apparatus according to a third embodiment.

FIG. 20 is a control flow executed in the image forming apparatusaccording to the third embodiment.

FIG. 21 illustrates an exposure distribution on a photosensitive drum inan image forming apparatus of related art.

DESCRIPTION OF EMBODIMENTS First Embodiment

An embodiment of an electrophotographic color image forming apparatus asan example is described below. It is to be noted that the embodiment isnot limited to the color image forming apparatus, and may be amonochrome image forming apparatus.

FIG. 1 is a schematic cross-sectional view of the color image formingapparatus. The color image forming apparatus shown in FIG. 1 includes areading device 22. The reading device 22 includes an ADF 18 (AutoDocument Feeder), a document plate 19, a reflecting mirror group 20, andan image sensor 21. The ADF 18 conveys a document set at a predeterminedposition to the document plate 19. The reading device 22 includes anilluminating device (not shown). The illuminating device irradiates adocument conveyed to the document plate 19 from the ADF 18 or a documentplaced on the document plate 19 with light. The light reflected from thedocument is guided by the reflecting mirror group 20 to the image sensor21. The image sensor 21 includes a CCD being a photoelectric conversionelement. The CCD generates read image data receiving the reflectedlight.

The image forming apparatus according to this embodiment includes twocassette paper feed portions 1 and 2, and a single manual paper feedportion 3. Recording sheets S (recording media) are fed selectively fromthe paper feed portions 1, 2, and 3. The recording sheets S are stackedin a cassette 4 or 5, or on a manual feed tray 6 of the paper feedportion 1, 2, or 3. The recording sheets S are successively picked up bya pickup roller 7 provided at each of the respective paper feedportions. Then, among the recording sheets S picked up by the pickuproller 7, a recording sheet S at the top of a bundle of recording sheetsis sent by a separation roller pair 8 including a feed roller 8A and aretard roller 8B to a registration roller pair 12. In this case, arecording sheet S fed from one of the cassettes 4 and 5 arranged atlarge distances from the registration roller pair 12 is relayed by aplurality of conveying roller pairs 9, 10, and 11 and then is sent tothe registration roller pair 12.

When the leading edge of the recording sheet S sent to the registrationroller pair 12 contacts a nip of the registration roller pair 12 andforms a predetermined loop, the movement of the recording sheet S istemporarily stopped. With the formation of this loop, a skew state ofthe recording sheet S is corrected.

A long intermediate transfer belt (endless belt) 13 being anintermediate transfer member is arranged downstream of the registrationroller pair 12. The intermediate transfer belt 13 is wound around adriving roller 13 a, a second transfer opposite roller 13 b, and atension roller 13c with a tension, so as to have a substantiallytriangular shape in cross-sectional view. The intermediate transfer belt13 rotates clockwise in the drawing. A plurality of photosensitive drums14, 15, 16, and 17 are arranged on an upper surface of a horizontalportion of the intermediate transfer belt 13 along the rotationdirection of the intermediate transfer belt 13. The photosensitive drums14, 15, 16, and 17 are photosensitive members that respectively beartoner images of different colors.

The photosensitive drum 14 at the most upstream side in theintermediate-transfer-belt rotation direction bears a toner image ofmagenta color, the next photosensitive drum 15 bears a toner image ofcyan color, the next photosensitive drum 16 bears a toner image ofyellow color, and the photosensitive drum 17 at the most downstream sidebears a toner image of black color.

Reference signs LM, LC, LY, LB denote optical scanning devices (laserscanners) respectively corresponding to the photosensitive drums 14, 15,16, and 17.

Next, an image forming process is described. The most upstreamphotosensitive drum 14 is exposed to laser light LM based on image dataof a magenta component. When the laser light LM scans the photosensitivedrum 14, an electrostatic latent image is formed on the photosensitivedrum 14. This electrostatic latent image is developed with a toner ofmagenta color supplied from a developing unit 23.

The photosensitive drum 15 is exposed to laser light LC based on imagedata of a cyan component. When the photosensitive drum 15 is exposed tothe laser light LC, an electrostatic latent image is formed on thephotosensitive drum 15. This electrostatic latent image is developedwith. a toner of cyan color supplied from a developing unit 24.

The photosensitive drum 16 is exposed to laser light LY based on imagedata of a yellow component. When the photosensitive drum 16 is exposedto the laser light LY, an electrostatic latent image is formed on thephotosensitive drum 16. This electrostatic latent image is developedwith a toner of yellow color supplied from a developing unit 25.

The photosenstive drum 17 is exposed to laser light LB based on imagedata of a black component. When the photosensitive drum 17 is exposed tothe laser light LB, an electrostatic latent image is formed on thephotosensitive drum 17. This electrostatic latent image is developedwith a toner of black color supplied from a developing unit 26.

First charging units 27 to 30 for electrically uniformly charging therespective photosensitive drums 14 to 17, cleaners 31 to 34 for removingtoners adhering on the photosensitive drums 14 to 17 after transfer ofthe toner images, and other members are arranged around the respectivephotosensitive drums 14 to 17.

The toner images on the photosensitive drums pass through transferportions between the intermediate transfer belt 13 and thephotosensitive drums 14 to 17. The toner images on the respectivephotosensitive drums are transferred on the intermediate transfer belt13 by a transfer bias applied by transfer charging units 90 to 93.

Then, the registration roller pair 12 starts rotating with regard to atiming at which the toner images on the intermediate transfer belt 13are aligned with the leading edge of the recording sheet. Theregistration roller pair 12 conveys the recording sheet S to a secondtransfer portion T2 between a second transfer roller 40 and a secondtransfer opposite roller 13b. At the second transfer portion T2, thetoner images on the intermediate transfer belt 13 are transferred on therecording sheet S by a transfer bias applied to the second transferroller 40.

The recording sheet S passing through the second transfer portion T12 issent to a fixing device 35 by the intermediate transfer belt 13. Then,in a process in which the recording sheet S passes through a nip portionformed by a fixing roller 35A and a pressing roller 35B in the fixingdevice 35, the toner images on the recording sheet S are heated by thefixing roller 35A, pressed by the pressing roller 35B, and hence fixedto the recording sheet surface. The recording sheet S after therecording sheet S passes through the fixing device 35 and is appliedwith the fixing processing is sent by a conveying roller pair 36 to adischarge roller pair 37, and is further discharged on a discharge tray38 arranged outside the apparatus.

FIG. 2 is a schematic configuration diagram of one of optical scanningdevices 101, 102, 103, and 104. The respective optical scanning deviceshave the same configuration, and hence, FIG. 2 exemplary shows theoptical scanning device 101. In FIG. 2, diverged laser light emittedfrom a laser light source 300 is collimated by a collimator lens 301 tobe substantially parallel light, and the passing amount of the laserlight is limited by an aperture 302. Thus, the laser light is shaped.The laser light passing through the aperture 302 is incident on a beamsplitter 308. The beam splitter 308 separates the laser light passingthrough the aperture 302 into laser light to be incident on a photodiode309 (hereinafter, PD 309) and laser light directed to a rotatablepolygonal mirror 305 (hereinafter, polygonal mirror 305). The PD 309outputs a detection signal of a value corresponding to the lightquantity of the laser light in response to reception of the laser light.A laser drive 310 executes feedback control for the light quantity ofthe laser light in accordance with the detection signal from the PD 309.The laser drive 310 is controlled for light emission with alight-emission control signal 318 from a CPU 212 (described later).

The laser light passing through the beam splitter 308 passes through acylindrical lens 303 and is incident on the polygonal mirror 305. Thepolygonal mirror 303 has a plurality of reflection surfaces. Thepolygonal mirror 305 rotates in arrow A direction when driven by a motor301. The polygonal mirror 305 deflects the laser light incident on thereflection surfaces so that the laser light scans the photosenstive drum14 in arrow B direction. The laser light deflected by the polygonalmirror 305 is transmitted through an imaging optical system (fθ lens)306 having fθ characteristics, and is guided onto the photosensitivedrum 14 through a mirror 307.

The optical scanning device 101 includes a Beam Detector 312(hereinafter, BD 312) being synchronization-signal generating means. TheBD 312 is arranged in a scanning path of the laser light, at a positionoutside an image formation region on the photosensitive drum 14. The BD312 generates a horizontal synchronization signal 317 when receiving thelaser light deflected by the polygonal mirror 305. The horizontalsynchronization signal 317 is input to the CPU 212. The CPU 212transmits an acceleration signal or a deceleration signal being acontrol signal 316 in FIG. 2 to a motor drive 313 so that the horizontalsynchronization signal 317 meets a reference period corresponding to atarget speed of the polygonal mirror 305 and the phase relationship withrespect to a polygonal mirror included in other optical scanning devicebecomes a predetermined phase relationship. The motor drive 313accelerates the rotation speed of the motor 304 on the basis of theacceleration signal and decelerates the motor 304 on the basis of thedeceleration signal.

Also, the CPU 212 controls an emission timing of laser light based onimage data from the laser light source 300 in accordance with thehorizontal synchronization signal 307. The CPU 212 includes a counter(not shown) that resets its count in response to the input of thehorizontal synchronization signal 307, and starts counting a clocksignal (described later) from the reset state. The CPU 212 controls animage processor (described later) and the laser drive 310 on the basisof the count value of the counter.

FIG. 3 is a block diagram showing the image processor and the laserdrive 310 included in the image forming apparatus according to thisembodiment. The image processor shown in FIG. 3 includes a clockgenerator 506 that generates a clock signal. Respective blocks(described later) execute respective processing in synchronization withthe clock signal. The clock signal is a signal with a higher frequencythan that of the horizontal synchronization signal. A read imageprocessor 501 receives read image data from the image sensor 21 andconverts the received signal into image data corresponding to therespective colors. Also, the read image processor 501 executesconversion. processing of converting the read image data into pixel datacorresponding to an output image and screen processing corresponding tothe respective colors.

A controller 502 writes the image data processed by the read imageprocessor 501 in a memory 505, reads out the written image data, andinputs the image data to an exposure modulator 503. The exposuremodulator 503 processes the image data input from the controller 502(the details are described later), and outputs the processed image datato a pattern converge 508. The pattern converter 508 converts the imagedata processed by the exposure modulator 503 into a bit pattern beingbinary data. The pattern converter 508 outputs the bit pattern (outputbit data in parallel) to a parallel/serial converter 504 insynchronization with the clock signal. The clock generator 506 generatesa PWM signal by outputting the bit data in serial in synchronizationwith a multiplied clock signal that is multiplied by a Phase Locked Loop507 (PLL 507). The laser drive 310 controls the laser light source 300to be lit or non-lit in accordance with the PWM signal.

Now, an exposure intensity distribution of the laser light on thephotosensitive drum is described. FIG. 6(a) shows an exposure intensitydistribution (hereinafter, abbreviated as exposure distribution)centered at a target pixel being a single pixel exposed to light whenthe surface of the photosensitive drum is exposed to light by a quantityof light corresponding to a single pixel by scanning with the laserlight on the surface of the photosensitive drum. In FIG. 6(a), thehorizontal axis indicates the number of pixels and the vertical axisindicates the exposure amount. FIG. 6(a) shows one-dimensional spread ofthe exposure distribution. The center coordinate 0 corresponds to thetarget pixel. Although depending on the design of the optical system,the exposure distribution has a tendency of a substantiallytwo-dimensional gauss distribution as shown in FIG. 6(a). Also, it isfound that the spread of the exposure distribution centered at thetarget pixel is a spread extending to several tens of pixels locatedaround the target pixel, for example, in a system with the resolution of2400 dpi, through the results of a simulation and an experiment.

The influence on the image frequency by the spread of the spot can beobtained as a characteristic obtained by executing Fourier transform ona spread function. FIG. 6(b) shows the characteristics obtained byFourier transform of the waveform in FIG. 6(a). FIG. 6(b) shows thecharacteristics converted while the distance between pixels is assumedas 0.1. The horizontal axis indicates the spatial frequency, and thevertical axis indicates the intensity.

In contrast, in related art, correction has been provided by imageprocessing, for example, by previously providing image processing suchas high-range enhancement to decrease the influence on surroundingpixels. For example, nonlinear characteristics, such as the exposureamount, latent-image potential, and rising of laser light, have beenconverted with LUT 1 and LUT 2, and corrected with a two-dimensionalfilter using a fixed filter coefficient.

However, due to an increase in resolution of an output image, theexposure range of a single pixel has affected. surrounding pixels andthe shape of the exposure spot at each position in the main-scanningdirection has not been uniform. Hence, the two-dimensional filter ofrelated art could not have provided sufficient correction.

To address such a problem, the image forming apparatus according to thisembodiment corrects image data by using a correction filter (correctionparameter) in the exposure modulator 503 shown in FIG. 3 to restrictunevenness of the exposure intensity distribution (potentialdistribution of electrostatic latent image) at each position in themain-scanning direction. The exposure modulator 503 corrects thegradation of an image by using a LUT 2001 (Look Up Table 2001), executesprocessing by using a two-dimensional filter, and corrects the linearityof the output of laser light caused by transient characteristics beingde vice characteristics of the laser drive 310 and the laser lightsource 300 by using a LUT 2003 (LookUp Table 2003).

Now, the linearity of the output of the laser light caused by thetransient characteristics is described. FIG. 5(a) shows input/outputsignals of the laser drive 310. The horizontal axis indicates the timeand the vertical axis indicates the signal voltage. FIG. 5(a) shows anoutput waveform of laser light for the input of a PWM signal withDuty=15%, an output waveform of laser light for the input. of a PWMsignal with Duty=50%, and an output waveform of laser light for theinput of a PWM signal with Duty=85%. Also, reference signs T15, T50, andT85 in FIG. 5(a) indicate periods with a pulse of a PWM signal beingHigh. Reference signs T15′, T50′, and T85′ indicate widths of outputwaveforms of laser light for the inputs of the PWM signals of the pulsesin T15, T50, and T85. It is to be noted that Duty represents a ratio ofthe period being High to the period of PHM.

As shown in FIG. 5(a), if the PWM signal with Duty=15% is input to thelaser drive 310, the PWM signal is changed to Low while the outputwaveform of the laser light is changed to High due to the transientcharacteristics of the laser drive 310 and the laser light source, andhence the pulse of the output waveform of the laser light is narrowedand becomes equivalent to a dotted-line waveform (T15>T15′). If the PWMsignal with Duty=85% is input to the laser drive 310, the PWM signal ischanged to High while the output waveform of the laser light is changedto Low, the time width of the Low period is narrowed and becomesequivalent to a dotted-line waveform (T85<T85′). In case of Duty=50%,the pulse width is not changed even with the transient characteristics(T50=T50′). In this way, the input of the PWM signal is not proportionalto Duty of the output waveform of the laser light.

The left drawing of FIG. 5(b) is a graph continuously plotting therelationship between the input of the PWM signal and the output of thelaser light. The vertical axis in the left drawing of FIG. 5(b)indicates the input pulse width of the PWM signal shown in FIG. 5(a),and the vertical axis is the pulse width of the output waveform of thelaser light. As shown in the left drawing of FIG. 5(b), the relationshipbetween the input pulse width of the PWM signal and the pulse width ofthe output waveform of the laser light is not linear. If therelationship between the input pulse width of the PWM signal and thepulse width of the output waveform of the laser light is not linear, thelinearity of the image density is decreased.

Therefore, the image forming apparatus of this embodiment ensures thelinearity of the output of laser light by correcting image data by usinga LUT (Look Up Table) in the right drawing of FIG. 5(b) being acorrection parameter having the inverted characteristics of the leftdrawing of FIG. 5(b) in the LUT 2003.

Next, correction using a two-dimensional filter 2002 in the exposuremodulator 503 is described with reference to FIGS. 4 and 7 to 11. FIGS.4. 10, and 11 respectively show an inner configuration of the exposuremodulator 503, filter coefficients (correction parameters) of a targetpixel and surrounding pixels of the two-dimensional filter 2002, and aninner configuration of the two-dimensional filter 2002.

As shown in FIG. 4, image data with the gradation corrected by the LUT2001 is input to the two-dimensional filter. The two-dimensional filter2002 corrects image data of a target pixel by using filter coefficientsrespectively assigned to a target pixel k(0, 0) and surrounding pixelsk(m, n) located around the target pixel at the center. FIG. 10 is amatrix of 15×15 filter coefficients indicating the filter coefficientsof the target pixel k(0, 0) and the surrounding pixels k(m, n).

The image forming apparatus according to this embodiment generatesfilter coefficients respectively corresponding to the target pixel andthe surrounding pixels as follows. The exposure modulator 503 includes amain-scanning counter 2005, a main-scanning variance profile memory2006, a sub-scanning variance profile memory 2007, a main/sub covarianceprofile memory 2008, and a filter coefficient generator 2004.

The exposure distribution of laser light on the photosensitive drum inthe image forming apparatus of this embodiment is determined by avariance value determined by an optical system including a lens, amirror, and a polygonal mirror of the optical scanning device and theconfiguration of the apparatus. To be specific, depending on the opticalsystem including the lens, mirror, and polygonal mirror of the opticalscanning device and the configuration of the apparatus, a variance valueσx (first variance value) in the main-scanning direction (hereinafter, zdirection), a variance value σy (second variance value) in thesub-scanning direction (hereinafter, y direction), and a covariancevalue pxy (third variance value) in the x direction and y direction aredetermined. The exposure distribution of laser light on thephotosensitive drum is determined by the following expression.

$\begin{matrix}{{f( {x,y} )} = {\frac{1}{2{\pi \cdot \sigma_{x}}\sigma_{y}\sqrt{1 - \rho_{xy}^{2}}}\exp{\quad( {{- \frac{1}{2( {1 - \rho_{xy}^{2}} )}} \cdot ( {( \frac{x}{\sigma_{x}} )^{2} + ( \frac{y}{\sigma_{y}} )^{2} - {2{\rho_{xy} \cdot ( \frac{x}{\sigma_{x}} )}( \frac{y}{\sigma_{y}} )}} )} )}}} & \lbrack {{Math}.\mspace{14mu} 1} \rbrack\end{matrix}$Expression 1

The variance values σx and σy, and covariance value pxy are valuesindicative of the exposure distribution centered at the target pixel onthe photosensitive drum, and the value varies depending on a position xin the main-scanning direction. Hence, when the image forming apparatusis assembled and adjusted in the factory, variance profiles σx(x),σy(x), and ρxy(x) are generated by measuring respective variance valuesat respective positions in the main-scanning direction. Themain-scanning variance profile σx(x) being the profile of the variancevalue σx in the main-scanning direction is stored in the main-scanningvariance profile memory 2006. The sub-scanning variance profile σy(x)being the profile of the variance value σy in the sub-scanning directionis stored in the sub-scanning variance profile memory 2007. Thecovariance value profile ρxy(x) being the profile of the covariancevalue ρxy corresponding to both the main-scanning direction and thesub-scanning direction is stored in the main/sub covariance profilememory 2008.

The main-scanning counter 2005 is reset when receiving the input of thehorizontal synchronization signal 317, and starts counting the pulse ofthe clock signal from the reset state. The count value of themain-scanning counter 2005 is a value indicative of the position x inthe main-scanning direction. The scanning variance profile memory 2006,the sub-scanning variance profile memory 2007, and the main/subcovariance profile memory 2008 respectively output variance valuescorresponding to the count value of the main-scanning counter 2005, to adata generator 2015 of the filter coefficient generator 2004.

The filter coefficient generator 2004 includes the data generator 2015,a two-dimensional FFT 2013, a ROM 2014, an operation unit 2011, acorrection range designation unit 2012, a two-dimensional inverse FFT2010, and a window function 2009.

The data generator 2015 generates two-dimensional gauss distributiondata of the exposure distribution of laser light on the photosensitivedrum centered at the target pixel when the target pixel is exposed tolight, on the basis of the variance values σx and σy, and the covariancevalue pxy input in accordance with the count value of the main-scanningcounter 2005. That is, the data generator 2015 generates two-dimensionalgauss distribution data for every position or every ever plural blocks(regions) in the main-scanning direction, on the basis of the inputvariance values. The generator 2015 inputs the generated two-dimensionalgauss distribution data to the two-dimensional FFT 2013. Thetwo-dimensional FFT generates characteristic data of a spatial frequencyby executing fast Fourier transform on the two-dimensional gaussdistribution data input from the data generator 2015. Thetwo-dimensional FFT inputs the characteristic data (profile) obtainedthrough the conversion to the operation unit 2011.

FIGS. 7(a), 7(b), and 7(c) are examples of characteristic data input bythe two-dimensional FFT 2013 to the operation unit 2011. In FIGS. 7(a),7(b), and 7(c), each axis indicates the angular frequency, and theinterpixel distance corresponds to 0.1. FIGS. 7(a), 7(b), and 7(c) showcharacteristic data by arithmetically operating the two-dimensionalgauss distribution data at respective positions (L2, C, R2) on thephotosensitive drum in the main-scanning direction shown in FIG. 21,into the spatial frequency. FIG. (a) shows characteristic data (DATA_1)of the exposure distribution in an end-portion region (L2) on thephotosensitive drum at the scanning start side in the main-scanningdirection. FIG. 7(b) shows characteristic data (DATA_C) of the exposuredistribution in a center region (C) on the photosensitive drum in themain-scanning direction. FIG. 7(c) shows characteristic data (DATA_R) ofthe exposure distribution in an end-portion region (R2) on thephotosensitive drum at the scanning end side in the main-scanningdirection.

The ROM 2014 stores reference characteristic data (target characteristicdata) of the exposure distribution. In the image forming apparatus ofthis embodiment, the exposure distribution in the center region (C) ofthe photosensitive drum in the main-scanning direction is assumed as anideal exposure distribution. Hence, DATA_C is held in the ROM 2014.During image formation, the ROM 2014 outputs DATE_C to the operationunit 2011 irrespective of the count value of the main-scanning counter2005.

The operation unit 2011 generates differential data based on thecharacteristic data input from the two-dimensional FFT 2013 and thereference characteristic data input from the ROM 2014. DATA_L-C shown inFIG. 8(a) is differential data obtained by subtracting DATA_C input fromthe ROM 2014 from DATA_L input from the two-dimensional FFT 2013.DATA_R-C shown in FIG. 8(b) is differential data obtained by subtractingDATA_C input from the ROM 2014 from DATA_R input from thetwo-dimensional FFT 2013. That is, DATA_L-C and DATA_R-C are dataindicative of differences in exposure distribution in the respectivescanning regions with respect to the exposure distribution being atarget. DATA_L-C and DATA_R-C indicate that, in the exposuredistribution in the end-portion region (L2) at the scanning start sidein the main-scanning direction and the exposure distribution in theend-portion region (R2) at the scanning end side in the main-scanningdirection, high-range characteristics at oblique portions in theshort-side direction of the ellipsoidal exposure distribution rise andhigh-range characteristics at oblique portions in the longitudinaldirection fall as compared with the exposure distribution of the centerregion (C) in the main scanning direction. Since the exposuredistribution at the center portion of the photosensitive drum serves asthe ideal exposure distribution, DATE_C-C (not shown) do not haveprotrusions or depressions.

Then, the operation unit 2011 generates correction data on the basis ofDATA_L-C in FIG. 8(a). That is, the operation unit 2011 generatescorrection data to decrease the difference indicated by DATA_L-C betweenDATA_L and DATA_C. Similarly, the operation unit 2011 generatescorrection data on the basis of DATA_R-C in FIG. 8(b). That is, theoperation unit 2011 generates correction data to decrease the differenceindicated by DATA_R-C between DATA_R and DATA_C.

When Ft (ωx, ωy) is a spatial frequency characteristic of a correctionobject and Fr(ωx, ωy) is a spatial frequency characteristic of areference, correction data K(ωx, ωy) is arithmetically operated by usingthe following functional expression.K(ωx, ωy)=Fr(ωx, ωy)/Ft(ωx, ωy)   Expression 2

The correction range designation unit 2012 designates and holds aspatial frequency with small correction effect, and clips the designatedrange as a range of predetermined values. In this embodiment, thespatial frequency is clipped at 0. FIG. 9 shows an example of correctiondata generated on the basis of operation data in FIG. 8(a), clipped bythe correction range designation unit 2012, and output from theoperation unit 2011. The operation unit 2011 inputs the correction data(FIG. 9) obtained by the arithmetic operation to the two-dimensionalinverse FFT.

The two-dimensional inverse FFT 2010 executes inverse frequencyconversion on the correction data input from the operation unit 2011 andgenerates correction parameters (filter coefficients) respectivelycorresponding to the target pixel and the surrounding pixels surroundingthe target pixel. FIG. 10 shows the correction parameters generated bythe two-dimensional inverse FF1 2010 and respectively corresponding tothe target pixel and the surrounding pixels in a matrix form. Charactersk (x, y) indicates a filter coefficient. The filter coefficient of thetarget pixel is k(0, 0). The filter coefficients in the matrix formshown in FIG. 10 indicate the amounts of change is potential at thetarget pixel position caused by exposure of the surrounding pixelslocated around the target pixel to laser light. The exposuredistribution in the image forming apparatus according to this embodimentis described as an example of correcting characteristics of apoint-symmetric distribution about the target pixel. Hence, the filtercoefficients k(x, y) are also point-symmetric about the target pixel.The two-dimensional inverse FFT 2010 inputs each filter coefficient k(x,y) to the window function processor 2009.

The window function processor 2009 outputs a filter coefficient kw(x, y)obtained by correcting the filter coefficient k(x, y) input from thetwo-dimensional inverse FFT 2010 by using a previously set windowfunction w(x, y). this embodiment, a hamming window is set for thewindow function w(x, y).kw(x, y)=w(x, y)*k(x, y)   Expression 3

The filter coefficient generator 2004 executes the above-describedprocessing for each pixel, and corrects image data on the basis of thefilter coefficient being correction data output from the window functionprocessor 2009 for each pixel in the two-dimensional filter 2002.Accordingly, even if the exposure distribution is different in themain-scanning direction, the unevenness in the main-scanning directionof the exposure intensity distribution. (potential distribution ofelectrostatic latent image) formed on the photosensitive drum can berestricted.

Next, an inner configuration of the two-dimensional filter 2002 isdescribed with reference to FIG. 11. The two-dimensional filter includesFIFOs (First In First Out Memories) 5001 to 5014, a shift register unit5015, a multiplier 5016, and an adder 5017.

As shown in FIG. 11, the 14 FIFOs 5001 to 5014 are connected in series,receive the input of image data from the LUT 2001 in synchronizationwith the image clock, and output the image data in the input order to ashift register unit 5003 in synchronization with the image clock. TheFIFOs 5001 to 5014 of this embodiment serve as a line memory buffer thatcan store image data by the number of pixels corresponding to a singlescanning period (single scanning line).

The shift register unit 5003 includes 15×15 registers. A plurality ofregisters D0_0 to D14_0 are assigned as shift. registers in a firststage. Shift register groups in second to fifteenth stages are similarlyconfigured. That is, the shift register unit 5003 includes the fifteenstages of the register groups. The FIFO memory 5001 in the first stageis connected to the register D0_0 of the shift resisters in the firststage, and inputs image data (pixel data) corresponding to a singlepixel to the register D0_0 in the input order. The FIFO memories in thesecond and later stages are respectively connected to the most upstreamregisters of the corresponding shift registers, and input image data(pixel data) each corresponding to a single pixel to the most upstreamregisters in the input order.

Also, the LUT 2001 is connected to the register 14_0 in the shiftregisters in the fifteenth stage. That is, the LUT 2001 inputs imagedata corresponding to a single pixel to the FIFO 5014 in the fourteenthstage and the register D14_0 in the shift registers in the fifteenthstage. The target pixel is data to he input to the register D7_7 in theshift register unit 5015.

A multiplier unit 5004 includes 15×15 multipliers M0_14 to M14_14. Therespective multipliers are individually provided respectively for theresisters in the shift register unit 5015 in a one-to-onecorrespondence. The multipliers receive inputs of image data eachcorresponding to a single pixel from the corresponding registers. Eachmultiplier receives the input of the filter coefficient output from thewindow function processor 2009 of the filter coefficient generator 2004.Each multiplier multiplies the image data by the input filtercoefficient. Then, each multiplier outputs the multiplied image data toan adder unit 3017.

The adder unit 3017 includes adders Ax: 0 to 14) and an adder A_ALL. Theadders Ax add the image data corresponding to a single pixel output fromeach of the multipliers M0_x to M14_H. The adder A_ALL adds the outputsfrom the adders Ax, and outputs the result as image data of the targetpixel to the LUT 2003.

In this way, by correcting the pixel data corresponding to the targetpixel by the two-dimensional filter 2002 with use of the filtercoefficients of the surrounding pixels, even if the exposuredistribution of laser light centered at the target pixel is differentdepending on the exposure region (or the exposure position) in themain-scanning direction on the photosensitive drum, the potentialdistribution of the electrostatic latent image centered at the targetpixel can be prevented from being uneven. For example, as shown in FIG.12(b), the unevenness in image quality of the output image in themain-scanning direction shown in FIG. 21 can be restricted irrespectiveof the screen angle (or the orientation of thin lines).

Second Embodiment

In this embodiment, a configuration that corrects image data, theconfiguration which is different from the second embodiment, isdescribed. The configuration other than the exposure modulator is thesame, and hence the description for the configuration other than theexposure modulator is omitted.

FIG. 13 shows a control block diagram of an image forming apparatusaccording to this embodiment. A ROM 1303 stores filter coefficientscorresponding to respective positions (or respective regions) in themain-scanning direction. The filter coefficients are filter coefficientsin a matrix centered at a target pixel and respectively correspond tothe target pixel and surrounding pixels data reading unit 1302 reads outthe filter coefficients in the matrix corresponding to the respectivepositions in the main-scanning direction from the ROM 1303 and writesthe filter coefficients in a register in a two-dimensional filter 1301,on the basis of the count value of the main scanning counter 2005. Thetwo-dimensional filter 1301 executes operation processing on image dataof the target pixel in accordance with the matrix coefficients, andgenerates the image data of the respective pixels.

Next, the operation processing executed by the two-dimensional filter1301 is described. The two-dimensional filter 1301 includes a firstoperation processor 1304 and a second operation processor 1305.

First operation processing executed by the first operation processor1304 is described first. By changing weighting of the exposure amountsof the target pixel and its surrounding pixels in accordance with thespot, shape at the target position, the exposure distribution based onthe image data of the target pixel is prevented from being unevenirrespective of the difference in spot shape at each position in themain-scanning direction. As illustrated, the first operation processor1301 obtains matrix coefficients M(a)={M(a)₁₁, M(a)₁₂, M(a)_(n), M(a)₂₁,M(a)₂₂, M(a)₂₃, M (a) M(a)₃₂M(a)₃₃}, and first operation result {₁₁,a₁₂, a_(n), a₂₁, a₂₂, a₂₃, a₃₃, a₃₃, a₃₃} which are obtained byintegrating density data I(a) of a target pixel a. An operationexpression of the first operation processing executed by the firstoperation processor is provided below.First operation result−I(a)×M(a)={I(a)×M(a)₁₁ , I(a)×M(a)₁₂ ,I(a)×Ml(a)₁₃ , I(a)×M(a)₂₁ , I(a)×M(a)₂₂ , I(a)=M(a)₂₃ , I(a)×M(a)₃₁ ,I(a)×M(a)₃₂ , I(a)×M(a)₃₃}  Expression 4

FIG. 14 shows the operation result for the pixel a after the operationprocessing. For example, as shown in FIG. 21(b), for a position like theend-portion region (L2) in the main-scanning direction at which the spotshape of laser light is thin and long from the upper left toward thelower right, filter coefficients are set to correct image data so thatthe exposure amounts of surrounding pixels at the lower left and upperright with respect to the target pixel are increased as compared withthe case without the correction using the filter coefficients. Incontrast, for a position like the end-portion region (R2) in themain-scanning direction at which the spot shape of laser light is thinand long from the lower left toward the upper right, filter coefficientsare set to correct image data so that the exposure amounts ofsurrounding pixels at the upper left and lower right are increased ascompared with the case without the correction using the filtercoefficients. It is to be noted that the first operation processing isexecuted on all pixels of a processing object image as shown in FIG.

The matrix coefficients used here are previously designed, for example,at adjustment in the factory, and stored in the ROM 1303. FIG. 16(a)shows an example of the filter coefficients in the matrix stored in theRPM 1303. At the time of shipment from the factory, CODs are arranged atpositions corresponding to the surface of the photosensitive drum, or ata plurality of positions (longitudinal direction) in the main-scanningdirection (the longitudinal direction of the photosensitive drum) by anumber n (n is a natural number) of points, and the spot shape of laserlight is measured at the plurality of positions. Then, matrixcoefficients {M(pi)₁₁, M(pi)₁₂, M(pi)₁₃, N(pi)₂₁, M(pi)₂₂, (pi)₂₃,N(pi)₃₁, N(pi)₃₂, N(pi)₃₃} corresponding to the measurement result atmeasurement positions pi (i is integers from 1 to n) in themain-scanning direction are calculated, and the matrix coefficients arestored in the memory 1303 in association with the measurement positionsPi. The filter coefficients shown in FIG. 16 represent amounts of changein potential at pixel positions of the surrounding pixels surroundingthe target pixel caused by exposure of the target pixel to light. It isto be noted that the measurement positions pi are values correspondingto the count value of the main-scanning counter.

In the first operation processing, the matrix coefficients correspondingto the longitudinal position of the target pixel are selected, andintegral processing is executed with density data. In this case,according to this embodiment, while the operation is executed by using3×3 matrix coefficients, the matrix size is determined to attain aneffect for the resolution and the spot size. FIGS. 16(b) and 16(c) eachshow the relationship between the resolution (pixel interval) and thespot size. If the spot size is large with respect to the pixel intervalas shown in FIG. 16(b), a plurality of spots overlap each other. In thiscase, by increasing the matrix size and executing an operation on pixelsincluding adjacent pixels and pixels next to the adjacent pixels, thelight quantity distribution can be corrected for a change in shape of alarger spot. Also, if spots on only pixels adjacent to the target pixeloverlap each other, spots on the pixels next to the adjacent pixels donot affect the light quantity distribution of the target pixel. Hence,3×3 matrix coefficients are used. As shown in FIG. 16(b), if the spotsize is substantially equivalent to the pixel interval, even though thelight quantities of the adjacent pixels are adjusted, the adjustmentless affects the light quantity distribution of the target pixel. Hence,the effect is small with the technique in this embodiment. Also, if thematrix size is increased, a memory is required for storing density dataof surrounding pixels used for the operation. The operation amount isincreased, and therefore the circuit scale is increased. Owing to this,the matrix size is desirable to be so small that the correction of thelight quantity distribution is effective.

Next, the second operation processing executed by the second operationprocessor 1305 is described with reference to FIG. 17. For example, whena pixel e is a target pixel, image data e₂₂ for the pixel e is generatedas shown in FIG. 15 by the first operation processing. Also, when pixelse are surrounding pixels, image data a₃₃, b₃₂, c₃₁, cl₇₃e₂₂, f₂₁, g₁₃,h₁₂, i₁₁ are generated for the pixels e. The second operation processor1305 executes an operation as follows as the second operation processingto obtain image data Ex (e) for the pixel e.Ex(e)=a ₃₃ +b ₃₂ +c ₃₁ +d ₂₃ +e ₂₂ +f ₂₁ +g ₁₃ +h ₁₂ +i ₁₁   Expression5

The second operation processor 1305 executes the second operationprocessing in Expression 5 on all pixels. Image data obtained for allpixels by the second operation processing is output to the LUT 2003.

By switching the filter coefficients in accordance with the exposureposition in the main-scanning direction and correcting the image data ofthe surrounding pixels, even if the spot shape of laser light on thephotosensitive drum in the main-scanning direction is not uniform, theunevenness of the exposure amount distribution in the main-scanningdirection can be restricted.

The configuration that obtains a result equivalent to the aforementionedexposure amount setting processing can be realized by filter processing.This filter processing is also included in the scope of the invention.The filter processing is described in detail. When Expression 5 thatcalculates the second operation result Ex(e) for a pixel e is deformed,the following expression is derived.Ex(e)=a ₃₃ +b ₃₂ +c ₃₁ +d ₂₃ +e ₂₂ +f ₂₁ +g ₁₃ +h ₁₂ +i ₁₁ =I(a)×M(a)₃₃+I(b)×M(b)₃₂ +I(c)×M(c)₃₁ +I(d)×M(d)₂₃ +I(e)×M(e)₂₂ +I(f)×M(f)₂₁+I(g)×M(g)₁₃ +I(h)×M(h)₁₂ +I(i)×M(i)₁₁   Expression 6.

This is filter processing that uses a filter {M(a)₃₃, M(b)₃₂, M(d)₃₁,M(d)₂₃, M(e)₂₂, M(f)₂₁, M(g)₁₃, M(h)₁₂, M(i)₁₁}, and calculates thelinear sum of density data {I(a), I(b), I(c), I(d), I(e), I(f), I(g),I(h), I(i)} of the target pixel and the surrounding pixels.

Also, in this embodiment, the exposure amount is controlled by changingthe lighting pulse width of the laser, that is, the emission time;however, it is not limited thereto. For another example, the exposureamount may be controlled by changing the light quantity of laser light,that is, the emission intensity (this may be also applied to the firstembodiment).

Also, in this embodiment, correcting the shape of the combined lightquantity distribution at a set of pixels including a target pixel andits surrounding pixels into a desirable shape is the purpose ofprocessing; however, the purpose of processing is not limited thereto.For another example, the purpose of processing may be correcting thegravity center position of the combined light quantity distribution at aset of pixels including a target pixel and its surrounding pixels into adesirable position. Accordingly, unevenness in image quality which mayoccur when the shift amount of the imaging position is differentdepending on the longitudinal position.

Third Embodiment

This embodiment relates to a technique of setting the exposure amount ofeach pixel on the basis of the previously measured spot shapes at plurallongitudinal positions similarly to the second embodiment. Inparticular, a point different from the second embodiment is described indetail.

In this embodiment, when the spot shape varies with a temperature changein the apparatus, proper correction is made in accordance with thetemperature. Members configuring optical scanning devices 101, 102, 103,and 104 are expanded (or contracted) due to a temperature change. Then,the optical path length until laser light reaches the surface of thephotosensitive drum is changed, and defocusing may occur. At this time,as shown in FIG. 18, the spot shape is changed in accordance with thedefocusing amount. As the defocusing is increased, the light intensityat the spot center is decreased and simultaneously the light intensityin the surrounding portion is increased. Hence, the spot shape becomeswide and defocused. To correct the change in spot shape due to thetemperature change, matrix coefficients corresponding to the spot shapewhen the temperature is changed are stored in the memory, the insidetemperature is measured by a measurement unit provided in the apparatus,and the matrix coefficients corresponding to the respective longitudinalpositions are set in accordance with the temperature change. FIG. 19shows a block diagram of a configuration including a thermistor 1903 inthe apparatus. The thermistor 1903 detects the inside temperature. Acontroller 1901 monitors the inside temperature at image formation. Ifthe temperature is changed to a predetermined value, the matrixcoefficients corresponding to the temperature are set on a laser basis.

The operation of the controller 1903 is described. Similarly to thesecond embodiment, it is assumed that initial matrix coefficients arewritten in the register of the first operation unit 1304 shown in FIG.13(b) immediately after the power supplied. Further, during a continuousjob, the inside temperature is repetitively monitored, and if atemperature change by a certain degree or more is made, the matrixcoefficients written in the register are updated. The operation of thecontroller during continuous job is shown in FIG. 20. In Step 1, whenstart of a print job is instructed, the controller 1901 startsmonitoring the temperature. The controller 1901 monitors the output fromthe thermistor 1903 in Step 2, and determines whether or not thetemperature change since previous monitoring exceeds a predeterminedthreshold in Step 3. In Step 3, if it is determined that the temperaturechange does not exceed the predetermined threshold, the controller 1901shifts the control to monitoring of the inside temperature in Step 2after a predetermined time interval elapses. If it is determined thatthe temperature change exceeds the predetermined threshold in Step 3,the controller 1901 starts setting filter coefficients in a matrix inStep 4. In Step 5, the controller 1901 determines the longitudinalposition on the basis of the count value of the main-scanning counter.In Step 6, the controller 1901 reads out the matrix coefficients basedon the determination result in Step 5 from the memory. An addresscorresponding to each position in each main-scanning direction isassigned to the ROM 1303, and filter coefficients in a matrixcorresponding to the inside temperature is stored in association withthe address. The controller 1901 reads out the filter coefficients inthe matrix corresponding to the temperature detected by the thermistor1901 and the longitudinal position in Step 6, and writes the read filtercoefficients in the matrix in the register in Step 7. In Step 8, thecontroller 1901 determines whether or not setting for all longitudinalpositions is ended. If it is determined that setting is ended, thecontrol is advanced to Step 9 in Step 9, the controller 1901 determineswhether or not the job is ended. If the job is not ended (the job iscontinued), the control is shifted to monitoring of the insidetemperature in Step 2. If it is determined that the lob is ended in Step8, the controller 1901 ends the setting operation for the filtercoefficients in the matrix.

In this embodiment, similarly to the second embodiment, filtercoefficients in a matrix are stored in the ROM 1301 in accordance withthe spot shape at each longitudinal position previously measured atadjustment in the factory. Also, a change in spot with respect to achange in inside temperature is previously measured, the filtercoefficients in the matrix are stored in association with thetemperature. The image forming apparatus according to the thirdembodiment can correct the change in spot shape due to the change ininside temperature, in addition to the variation in spot shape at thelongitudinal position in an initial phase as compared with the first andsecond embodiments.

In this embodiment, the filter coefficients in the matrix are set inaccordance with the detection result of the inside temperature. However,the detection object is not limited to the inside temperature. Forexample, the inside humidity or inside atmospheric pressure may bemeasured by a measurement unit 1902. For another example, the position,posture, speed, temperature, electric resistance, charge amount, drivecurrent, drive timing, etc., of any one of the members configuring theimage forming apparatus may be a detection object.

The present invention is not limited to the above-described embodiments,and various changes and modifications can be made without departing fromthe spirit ant scope of the present invention. Therefore, the followingclaims are attached for making the scope of the present invention inpublic.

The invention claimed is:
 1. An image forming apparatus, comprising: alight source configured to emit light beam for exposing a photosensitivemember to light; a deflecting unit configured to deflect the light beamso that the light beam scans the photosensitive member; an optical unitconfigured to guide the light beam deflected by the deflecting unit tothe photosensitive member; a data generating unit configured to generatepixel data corresponding to each pixel included in an output image; anoutputting unit configured to output correction data for correcting apotential distribution of an electrostatic latent image centered at atarget pixel formed on the photosensitive member due to a change of anexposure spot shape of the light beam on the photosensitive member is ascanning direction in which the light beam scans the photosensitivemember, wherein the outputting unit outputs the correction data forpixel data of the target pixel based on pixel data of surrounding pixelslocated around the target pixel, the correction data being set for eachof a plurality of regions of the photosensitive member in the scanningdirection, the outputting unit switching the correction data outputteddepending on the position of the target pixel in the scanning direction;a correcting unit configured to correct pixel data of the target pixelon the basis of the correction data and a plurality of pixel data of thesurrounding pixels surrounding the target pixel by using a twodimensional filter; and a control unit configured to control the lightsource on the basis of the pixel data of the target pixel corrected bythe correcting unit, to form the target pixel.
 2. The image formingapparatus according to claim 1, wherein the outputting unit includes astorage unit configured to store the correction data corresponding to aposition in the scanning direction.
 3. The image forming apparatusaccording to claim 1, further comprising: a storage unit configured to afirst variance value indicative of a potential distribution of theelectrostatic latent image centered at the target pixel in the scanningdirection, a second variance value indicative of a potentialdistribution of the electrostatic latent image centered at the targetpixel in a rotation direction of the photosensitive member, and a thirdvariance value indicative of a potential distribution of theelectrostatic latent image centered at the target pixel in both thescanning direction and the rotation direction; and a correction-datagenerating unit configured to generate the correction data on the basisof the first variance value, the second variance value, and the thirdvariance value.
 4. The image forming apparatus according to claim 1,wherein the correction parameter includes a parameter corresponding tothe target pixel and a plurality of correction parameters correspondingto the surrounding pixels, the correcting unit correcting the image dataon the basis of the two-dimensional filter output from the output unitin accordance with a position of the target pixel in the scanningdirection.
 5. The image forming apparatus according to claim 1, furthercomprising: a synchronization-signal generating unit configured toreceive the light beam deflected by the deflecting unit, and generatinga synchronization signal in response to the reception of the light beam;a clock-signal generating unit configured to generate a clock signalbeing a signal with a higher frequency than a frequency of thesynchronization signal; and a counter configured to count the clocksignal, wherein a count value of the counter is a value corresponding tothe position in the scanning direction, and wherein the outputting unitoutputs correction data corresponding to the count value on the basis ofthe count value of the counter.